I have a problem duplicating a Mesh and again applying curve modifiers to the copy correctly?
You've enabled the Object Offset of the Array modifier, with your curve as the offset object, is there a reason for that? Because it messes your object: as your curve is scaled 6 times, it will also scale your cube 6 times...

Object Offset will array your object taking account of the location, rotation and scale of the chosen object, like for example it will scale your original object increasingly if your offset object has been scaled, which is not what you want, you want a simple array, then a second modifier that makes the array follow a curve.

So disable this option as you just want your cube to be duplicated. It's the next modifier (Curve) that will take care of making your object following the curve.

Also, if you choose to apply the scale of your curve, don't forget, in Edit mode, to bring back the Radius of your curve vertices to 1 (on the N panel of your 3D view).